Year in, year out, Greg Osby leads one of the best quartets in jazz–namely himself, pianist Jason Moran, and whatever two other guys they bring along. It can’t be the easiest gig for a rhythm section to step into: the saxophonist glides between stressing downbeats and upbeats, sometimes in the same phrase, giving his momentum a curious surging instability, and he’ll skitter sideways through a chord progression like a car across six lanes of traffic. A while ago he began peppering his sets with jazz goldies like Lee Morgan’s “The Sidewinder” and Horace Silver’s “Song for My Father” in hopes that using familiar tunes as departure points would make his permutations easier to track. (It worked for Monk.) The repertoire also connects him with Blue Note stablemates who’ve combined soul with an active intelligence over the decades. There are a couple covers on his new Inner Circle (with Moran, bassist Tarus Mateen, drummer Eric Harland, and vibist Stefon Harris): Mingus’s ballad “Self-Portrait in Three Colors” and “All Neon Like,” by a composer jazz musicians are getting fond of, Bjork. (Moran and Dave Douglas have covered her too.) For the rest of the record, Osby devises pieces that set up fresh puzzles for individual or collective improvising. On “Entruption,” for instance, the band maintains a fluid rhythm despite a pause built into the melody every two bars–a hiccup it sticks with even when deep into the improvising. Moran–who takes on Schumann, James P. Johnson, and Afrika Bambaataa on his imminent solo disc, Modernistic (Blue Note)–has been Osby’s right-hand man for about five years, and they have that telepathic hookup jazz listeners live for. This time the other guys are drummer Damion Reid and the seasoned bassist Robert Hurst, who’s put in time with three Marsalises and Osby’s old M-Base collective. Osby likes playing the Green Mill because of its younger audience, and his periodic gigs there are worth straining to hear over the weekend party people. Friday, August 23, 9 PM, and Saturday, August 24, 8 PM, Green Mill, 4802 N. Broadway; 773-878-5552.

Art accompanying story in printed newspaper (not available in this archive): photo/Michael Jackson.